UCSS Math II 3A.2.4 Example 3

Factor , and then verify your results.
  1. Determine any common factors of the given trinomial, if common factors exist.
  2. Multiply , the coefficient of the second-degree term, by , the constant.
  3. List all of the possible factors for the product of and .
  4. Determine which set of factors has a sum that equals , the coefficient of the first-degree term.
  5. Rewrite , the first-degree term, as the sum of two terms.
  6. Group the terms of the new polynomial according to their common factors, if common factors exist.
  7. Factor out common factors from each set of grouped terms, and rewrite the expression from the previous step.
  8. Factor the expressions further to create matching binomial factors.
  9. Use the Distributive Property to rewrite the expression as two factors, and then write the result along with the GCF determined in step 1.
  10. Distribute the factors to verify that they result in the original trinomial.
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